Abstract : Discussed is research on a conventional ab initio LCAO SCF MO method, with a basis of atomic orbitals and inclusion of interactions among all electrons and nuclei; and an approach based on the recognition of the chemical divisions of the electronic structure into metal cores, ligand omega frameworks and the valence shell. Results available so far have allowed a complete test of all computer programs and have demonstrated the feasibility of both types of calculation. Also reported is research on perturbation theory - providing various alternative routes to the calculation of the structure and properties of many-electron systems. In particular it should permit the discussion of electronic properties within iso-electronic families of molecules in which the nuclear charges vary (e.g. as in changing the ligands or the metal in a complex). The use of perturbation theory leads to new theoretical problems, some of which are here investigation for the first time. Preliminary calculations on very simple systems have given encouraging numerical results. (Author)